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Likelihood-Based Confidence Sets for the Timing of Structural Breaks

  • Eo, Yunjong
  • Morley, James C.

In this paper, we propose a new approach to constructing confidence sets for the timing of structural breaks. This approach involves using Markov-chain Monte Carlo methods to simulate marginal “fiducial” distributions of break dates from the likelihood function. We compare our proposed approach to asymptotic and bootstrap confidence sets and find that it performs best in terms of producing short confidence sets with accurate coverage rates. Our approach also has the advantages of i) being broadly applicable to different patterns of structural breaks, ii) being computationally efficient, and iii) requiring only the ability to evaluate the likelihood function over parameter values, thus allowing for many possible distributional assumptions for the data. In our application, we investigate the nature and timing of structural breaks in postwar U.S. Real GDP. Based on marginal fiducial distributions, we find much tighter 95% confidence sets for the timing of the so-called “Great Moderation” than has been reported in previous studies.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 10372.

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Date of creation: 05 Sep 2008
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Handle: RePEc:pra:mprapa:10372
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  1. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-56, July.
  2. JAMES G. MacKINNON, 2006. "Bootstrap Methods in Econometrics," The Economic Record, The Economic Society of Australia, vol. 82(s1), pages S2-S18, 09.
  3. James G. MacKinnon, 2002. "Bootstrap inference in econometrics," Canadian Journal of Economics, Canadian Economics Association, vol. 35(4), pages 615-645, November.
  4. Donald W. K. Andrews, 2003. "Tests for Parameter Instability and Structural Change with Unknown Change Point: A Corrigendum," Econometrica, Econometric Society, vol. 71(1), pages 395-397, January.
  5. James H. Stock & Mark W. Watson, 1994. "Evidence on structural instability in macroeconomic times series relations," Working Paper Series, Macroeconomic Issues 94-13, Federal Reserve Bank of Chicago.
  6. James H. Stock & Mark W. Watson, 2003. "Has the Business Cycle Changed and Why?," NBER Chapters, in: NBER Macroeconomics Annual 2002, Volume 17, pages 159-230 National Bureau of Economic Research, Inc.
  7. Lutz Kilian, 1999. "Finite-Sample Properties of Percentile and Percentile-t Bootstrap Confidence Intervals for Impulse Responses," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 652-660, November.
  8. Christopher A. Sims & Tao Zha, 1994. "Error Bands for Impulse Responses," Cowles Foundation Discussion Papers 1085, Cowles Foundation for Research in Economics, Yale University.
  9. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
  10. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
  11. Eiji Kurozumi & Purevdorj Tuvaandorj, 2010. "Model Selection Criteria in Multivariate Models with Multiple Structural Changes," Global COE Hi-Stat Discussion Paper Series gd10-144, Institute of Economic Research, Hitotsubashi University.
  12. Zivot, Eric & Andrews, Donald W K, 1992. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 251-70, July.
  13. Bai, Jushan & Lumsdaine, Robin L & Stock, James H, 1998. "Testing for and Dating Common Breaks in Multivariate Time Series," Review of Economic Studies, Wiley Blackwell, vol. 65(3), pages 395-432, July.
  14. BAI, Jushan & PERRON, Pierre, 1998. "Computation and Analysis of Multiple Structural-Change Models," Cahiers de recherche 9807, Universite de Montreal, Departement de sciences economiques.
  15. Elliott, Graham & Muller, Ulrich K., 2007. "Confidence sets for the date of a single break in linear time series regressions," Journal of Econometrics, Elsevier, vol. 141(2), pages 1196-1218, December.
  16. Margaret McConnell & Gabriel Perez Quiros, 2000. "Output fluctuations in the United States: what has changed since the early 1980s?," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
  17. Timothy Cogley, . "How Fast Can the New Economy Grow? A Bayesian Analysis of the Evolution of Trend Growth," Working Papers 2133301, Department of Economics, W. P. Carey School of Business, Arizona State University.
  18. Bai, Jushan, 1999. "Likelihood ratio tests for multiple structural changes," Journal of Econometrics, Elsevier, vol. 91(2), pages 299-323, August.
  19. Jushan Bai, 1997. "Estimation Of A Change Point In Multiple Regression Models," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 551-563, November.
  20. Donald W.K. Andrews & Werner Ploberger, 1992. "Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative," Cowles Foundation Discussion Papers 1015, Cowles Foundation for Research in Economics, Yale University.
  21. Chang-Jin Kim & James Morley & Jeremy Piger, 2008. "Bayesian counterfactual analysis of the sources of the great moderation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(2), pages 173-191.
  22. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
  23. Francis X. Diebold & Celia Chen, 1993. "Testing structural stability with endogenous break point: a size comparison of analytic and bootstrap procedures," Working Papers 93-11, Federal Reserve Bank of Philadelphia.
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